compiler/stdc/math/s_casinf.c

   1 /*      $OpenBSD: s_casinf.c,v 1.3 2011/07/20 19:28:33 martynas Exp $   */
   2 /*
   3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   4  *
   5  * Permission to use, copy, modify, and distribute this software for any
   6  * purpose with or without fee is hereby granted, provided that the above
   7  * copyright notice and this permission notice appear in all copies.
   8  *
   9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  16  */
  17
  18 /*                                                      casinf()
  19  *
  20  *      Complex circular arc sine
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * void casinf();
  27  * cmplxf z, w;
  28  *
  29  * casinf( &z, &w );
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * Inverse complex sine:
  36  *
  37  *                               2
  38  * w = -i clog( iz + csqrt( 1 - z ) ).
  39  *
  40  *
  41  * ACCURACY:
  42  *
  43  *                      Relative error:
  44  * arithmetic   domain     # trials      peak         rms
  45  *    IEEE      -10,+10     30000       1.1e-5      1.5e-6
  46  * Larger relative error can be observed for z near zero.
  47  *
  48  */
  49
  50 #include <complex.h>
  51 #include "math.h"
  52
  53 float complex
  54 casinf(float complex z)
  55 {
  56         float complex w;
  57         float x, y;
  58         float complex ca, ct, zz, z2;
  59         /*
  60         float cn, n;
  61         static float a, b, s, t, u, v, y2;
  62         static cmplxf sum;
  63         */
  64
  65         x = crealf(z);
  66         y = cimagf(z);
  67
  68         if(y == 0.0f) {
  69                 if(fabsf(x) > 1.0f) {
  70                         w = (float)M_PI_2 + 0.0f * I;
  71                         /*mtherr( "casinf", DOMAIN );*/
  72                 }
  73                 else {
  74                         w = asinf (x) + 0.0f * I;
  75                 }
  76                 return (w);
  77         }
  78
  79         /* Power series expansion */
  80         /*
  81         b = cabsf(z);
  82         if(b < 0.125) {
  83                 z2.r = (x - y) * (x + y);
  84                 z2.i = 2.0 * x * y;
  85
  86                 cn = 1.0;
  87                 n = 1.0;
  88                 ca.r = x;
  89                 ca.i = y;
  90                 sum.r = x;
  91                 sum.i = y;
  92                 do {
  93                         ct.r = z2.r * ca.r  -  z2.i * ca.i;
  94                         ct.i = z2.r * ca.i  +  z2.i * ca.r;
  95                         ca.r = ct.r;
  96                         ca.i = ct.i;
  97
  98                         cn *= n;
  99                         n += 1.0;
 100                         cn /= n;
 101                         n += 1.0;
 102                         b = cn/n;
 103
 104                         ct.r *= b;
 105                         ct.i *= b;
 106                         sum.r += ct.r;
 107                         sum.i += ct.i;
 108                         b = fabsf(ct.r) + fabsf(ct.i);
 109                 }
 110                 while(b > MACHEPF);
 111                 w->r = sum.r;
 112                 w->i = sum.i;
 113                 return;
 114         }
 115         */
 116
 117
 118         ca = x + y * I;
 119         ct = ca * I;    /* iz */
 120         /* sqrt( 1 - z*z) */
 121         /* cmul( &ca, &ca, &zz ) */
 122         /*x * x  -  y * y */
 123         zz = (x - y) * (x + y) + (2.0f * x * y) * I;
 124         zz = 1.0f - crealf(zz) - cimagf(zz) * I;
 125         z2 = csqrtf (zz);
 126
 127         zz = ct + z2;
 128         zz = clogf (zz);
 129         /* multiply by 1/i = -i */
 130         w = zz * (-1.0f * I);
 131         return (w);
 132 }